The ends of a metallic metre stick are maintained at temperatures 200- C and 0- C- If one end of a metallic rod of same material is maintained at 20- C- where should its other end be kept in contact with metre stick so that there is no heat current in the rod in its steady state conduction-A- 95 cmB- 90 cm- 75 cmD- 60 cm

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Standard XII

Physics

Longitudinal Stress

The ends of a...

Question

The ends of a metallic metre stick are maintained at temperatures $200^{\circ} C$ and $0^{\circ} C$ . If one end of a metallic rod of same material is maintained at $20^{\circ} C,$ where should its other end be kept in contact with metre stick so that there is no heat current in the rod in its steady state conduction?

95 c m

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90 c m

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75 c m

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60 c m

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Solution

The correct option is B $90 c m$
If there is no heat current in lower rod, temperature of point $C$ should be $20^{\circ} C$ . For this,
$i = \frac{200 - θ_{c}}{R_{1}} = \frac{θ_{c} - 0}{R_{2}}$

$\Rightarrow \frac{200 - 20}{\frac{x}{K A}} = \frac{20 - 0}{\frac{(1 - x)}{K A}} \Rightarrow 180 [1 - x] = 20 x \Rightarrow 9 - 9 x = x \Rightarrow x = \frac{9}{10} m = 90 c m$

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The ends of a metallic metre stick are maintained at temperatures 200∘C and 0∘C. If one end of a metallic rod of same material is maintained at 20∘C, where should its other end be kept in contact with metre stick so that there is no heat current in the rod in its steady state conduction?

The correct option is B 90 cmIf there is no heat current in lower rod, temperature of point C should be 20∘C. For this, i=200−θcR1=θc−0R2 ⇒200−20xKA=20−0(1−x)KA⇒180[1−x]=20x⇒9−9x=x⇒x=910 m=90 cm